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Can anyone please tell me whether the existence of cointegration between two series necessarily implies Granger causality between their "first differences"? I'd appreciate it if you could explain your reason.

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  • $\begingroup$ yes. granger causality says that, if including X in a model, improves ones prediction of Y, then X granger causes Y. In the case of cointegration, the ECM formulation shows explicitly that knowing $(X_t - X_{t-1})$ improves the prediction of $(Y_t - Y_{t-1})$ which are both first differences. $\endgroup$
    – mlofton
    Apr 22 at 11:02
  • $\begingroup$ @mlofton, it is always good to emphasize that Granger causality deals with incremental improvement in prediction accuracy once lags of $Y$ have been conditioned on. I have seen too many instances where people forget that and then incorrectly conclude that e.g. early-morning bird songs Granger-cause sunrise... $\endgroup$ Apr 22 at 11:38
  • $\begingroup$ @Richard Hardy: Yes, I hope that I said that sort of but probably did not give it enough emphasis. The interesting thing about cointegration ( atleast in the engle-granger case where there are just two variables ) is that, as the OP said, the first difference of $X_t$ granger causes the first difference of $Y_t$. I never thought of it that way until I read the question. $\endgroup$
    – mlofton
    Apr 22 at 20:14
  • $\begingroup$ Does this vary with the type of cointegration used? For example I am learning it in the context of the ARDL bounds test. Not the Engel Granger method (and still understand the concept very generally at best). I know these two approaches are quite different. $\endgroup$
    – user54285
    Apr 22 at 21:56
  • $\begingroup$ A quotation from Dave Giles blog: "If two or more time-series are cointegrated, then there must be Granger causality between them - either one-way or in both directions. However, the converse is not true.". The blog post is very well written – go ahead and read it. Perhaps you will find the answer to your question as well. $\endgroup$ Apr 23 at 5:30

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